The report states that the Black Eagles have struck a three-year deal with the Colombian international.
Zapata’s contract with AC Milan expires at the end of the seaosn which means he is free to discuss terms with any club.
Everton have also been linked with the experinced midfielder by the Daily Mail newspaper. The daily paper states that Zapata is on Everton’s list of targets should they lose their fight to keep John Stones.
Zapata, 28, was used sparingly by Milan last season and is expected to leave at the end of the season.
Besiktas are on the hunt for extra defensive cover after offloading Ersan Gulum in January.
The Black Eagles have been forced to use Necip and Tosic as centre backs due to injures.